GUDHI Project           Software for Geometry Understanding in Higher Dimensions

Participants           GUDHI, people.

Description The GUDHI library is a generic open source C++ library, with a Python interface, for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding. The library offers state-of-the-art data structures and algorithms to construct simplicial complexes and compute persistent homology. The library comes with data sets, demos, examples and test suites.

Documentation on the project webpage        Cite Acknowledging the GUDHI library

Contributions to the software project    

  • Clément Maria - Filtered Complexes: package to encode simplicial complexes, implementing the Simplex Tree data structure.

  • Clément Maria - Persistent Cohomology: package to compute persistence diagrams, based on the Compressed Annotation Matrix implementation of the persistent cohomology algorithm.

  • Clément Maria, Jean-Daniel Boissonnat, Marc Glisse, Mariette Yvinec - The Gudhi Library: Simplicial Complexes and Persistent Homology: article published in the Proceedings of the International Congress on Mathematical Software (ICMS) 2014 describing the software library.

  • The R package TDA           Statistical Tools for Topological Data Analysis

    Authors           Brittany T. Fasy, Jisu Kim, Fabrizio Lecci, Clément Maria and Vincent Rouvreau

    Description Tools for the statistical analysis of persistent homology and for density clustering. For that, this package provides an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus, and PHAT.

    Documentation           article "Introduction to the R package TDA"

    Regina Project           Software for Low-Dimensional Topology

    Authors           Benjamin A. Burton, Ryan Budney, William Pettersson and others.

    Description Regina is a software package for 3-manifold and 4-manifold topologists, with a focus on triangulations, normal surfaces and angle structures. For 3-manifolds, it includes high-level tasks such as 3-sphere recognition, connected sum decomposition and Hakenness testing, comes with a rich database of census manifolds, and incorporates the SnapPea kernel for working with hyperbolic manifolds. For 4-manifolds, it offers a range of combinatorial and algebraic tools, plus support for normal hypersurfaces. Regina comes with a full graphical user interface, as well as Python bindings and a low-level C++ programming interface.

    Contributions to the software project    

  • I am currently working on the implementation of our work, with Ben Burton and Jonathan Spreer, on the computation of Turaev-Viro invariants of 3-manifolds.